Blockmodeling

Blockmodeling is a set or a coherent framework, that is used for analyzing social structure and also for setting procedure(s) for partitioning (clustering) social network's units (nodes, vertices, actors), based on specific patterns, which form a distinctive structure through interconnectivity.

As an empirical procedure, blockmodeling assumes that all the units in a specific network can be grouped together to such extent to which they are equivalent.

While some contend that the blockmodeling is just clustering methods, Bonacich and McConaghy state that "it is a theoretically grounded and algebraic approach to the analysis of the structure of relations".

[5]: 2, 3  According to Batagelj, the primary "goal of blockmodeling is to reduce a large, potentially incoherent network to a smaller comprehensible structure that can be interpreted more readily".

Real-world networks can be large and complex; blockmodeling is used to simplify them into smaller structures that can be easier to interpret.

A block (also blockmodel) is defined as a submatrix, that shows interconnectivity (links) between nodes, present in the same or different clusters.

[11]: 8 A matrix representation of a graph is composed of ordered units, in rows and columns, based on their names.

[8] The primary objective of the matrix form is to visually present relations between the persons included in the cluster.

[2] With blockmodeling, it is necessary to consider the issue of results being affected by measurement errors in the initial stage of acquiring the data.

[3][5]: 24 Indirect blockmodeling approaches, where partitioning is dealt with as a traditional cluster analysis problem (measuring (dis)similarity results in a (dis)similarity matrix), are:[8][2] According to Brusco and Steinley (2011),[14] the blockmodeling can be categorized (using a number of dimensions):[15] Blockmodels (sometimes also block models) are structures in which: Computer programs can partition the social network according to pre-set conditions.

Different characteristics of social networks. A, B, and C show varying centrality and density of networks; panel D shows network closure, i.e., when two actors, tied to a common third actor, tend to also form a direct tie between them. Panel E represents two actors with different attributes (e.g., organizational affiliation, beliefs, gender, education) who tend to form ties. Panel F consists of two types of ties: friendship (solid line) and dislike (dashed line). In this case, two actors being friends both dislike a common third (or, similarly, two actors that dislike a common third tend to be friends).
In graph theory , the image provides a simplified view of a network, where each of the numbers represents a different node.
Structural equivalence
Regular equivalence